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E-raamat: Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi Equations

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(Ecole Polytechnique, Montreal, Canada)
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  • Ilmumisaeg: 19-Dec-2017
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781351833219
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Nonlinear H-Infinity Control, Hamiltonian Systems and Hamilton-Jacobi EquationsSuurem pilt
  • Formaat: EPUB+DRM
  • Ilmumisaeg: 19-Dec-2017
  • Kirjastus: CRC Press Inc
  • Keel: eng
  • ISBN-13: 9781351833219
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Aliyu (Ecole Polytechnique de Montreal) develops equations for state-feedback and output-feedback problems in continuous-time affine nonlinear time-invariant systems, discrete-time nonlinear control problems, and non-linear sub-optimal filtering problems. The final chapter introduces algorithms for solving Hamilton-Jacobi equations. This graduate textbook is intended for courses in robust and optimal control of nonlinear systems for electrical, mechanical, aerospace, and industrial engineering. Annotation ©2011 Book News, Inc., Portland, OR (booknews.com)

A comprehensive overview of nonlinear H8 control theory for both continuous-time and discrete-time systems, Nonlinear H8-Control, Hamiltonian Systems and Hamilton-Jacobi Equations covers topics as diverse as singular nonlinear H8-control, nonlinear H8 -filtering, mixed H2/ H8-nonlinear control and filtering, nonlinear H8-almost-disturbance-decoupling,

and algorithms for solving the ubiquitous Hamilton-Jacobi-Isaacs equations. The link between the subject and analytical mechanics as well as the theory of partial differential equations is also elegantly summarized in a single chapter.

Recent progress in developing computational schemes for solving the Hamilton-Jacobi equation (HJE) has facilitated the application of Hamilton-Jacobi theory in both mechanics and control. As there is currently no efficient systematic analytical or numerical approach for solving them, the biggest bottle-neck to the practical application of the nonlinear equivalent of the H8-control theory has been the difficulty in solving the Hamilton-Jacobi-Isaacs partial differential-equations (or inequalities). In light of this challenge, the author hopes to inspire continuing research and discussion on this topic via examples and simulations, as well as helpful notes and a rich bibliography.

Nonlinear H8-Control, Hamiltonian Systems and Hamilton-Jacobi Equations was written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management.

Arvustused

"This book is a comprehensive overview of nonlinear H-control theory for both continuous-time and discrete-time systems. ... The book can be used for a specialized or seminar course in robust and optimal control of nonlinear systems. It is written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management. I believe that this book will be cited in many future works in the field of H-control theory." Vasile Drgan (Bucharest), Mathematical Reviews, 2012D "This book is a comprehensive overview of nonlinear H-control theory for both continuous-time and discrete-time systems. ... The book can be used for a specialized or seminar course in robust and optimal control of nonlinear systems. It is written for practicing professionals, educators, researchers and graduate students in electrical, computer, mechanical, aeronautical, chemical, instrumentation, industrial and systems engineering, as well as applied mathematics, economics and management. I believe that this book will be cited in many future works in the field of H-control theory." Vasile Drgan (Bucharest), Mathematical Reviews, 2012D

1 Introduction
1(26)
1.1 Historical Perspective on Nonlinear H∞-Control
2(2)
1.2 General Set-Up for Nonlinear H∞-Control Problems
4(14)
1.2.1 Mixed H2/H∞-Control Problem
12(2)
1.2.2 Robust H∞-Control Problem
14(1)
1.2.3 Nonlinear H∞-Filtering
15(1)
1.2.4 Organization of the Book
16(2)
1.3 Notations and Preliminaries
18(8)
1.3.1 Notation
18(2)
1.3.2 Stability Concepts
20(6)
1.4 Notes and Bibliography
26(1)
2 Basics of Differential Games
27(16)
2.1 Dynamic Programming Principle
27(3)
2.2 Discrete-Time Nonzero-Sum Dynamic Games
30(4)
2.2.1 Linear-Quadratic Discrete-Time Dynamic Games
32(2)
2.3 Continuous-Time Nonzero-Sum Dynamic Games
34(6)
2.3.1 Linear-Quadratic Continuous-Time Dynamic Games
36(4)
2.4 Notes and Bibliography
40(3)
3 Theory of Dissipative Systems
43(36)
3.1 Dissipativity of Continuous-Time Nonlinear Systems
44(10)
3.1.1 Stability of Continuous-Time Dissipative Systems
51(1)
3.1.2 Stability of Continuous-Time Dissipative Feedback-Systems
52(2)
3.2 L2-Gain Analysis for Continuous-Time Dissipative Systems
54(2)
3.3 Continuous-Time Passive Systems
56(6)
3.4 Feedback-Equivalence to a Passive Continuous-Time Nonlinear System
62(3)
3.5 Dissipativity and Passive Properties of Discrete-Time Nonlinear Systems
65(4)
3.6 l2-Gain Analysis for Discrete-Time Dissipative Systems
69(3)
3.7 Feedback-Equivalence to a Discrete-Time Lossless Nonlinear System
72(5)
3.8 Notes and Bibliography
77(2)
4 Hamiltonian Mechanics and Hamilton-Jacobi Theory
79(24)
4.1 The Hamiltonian Formulation of Mechanics
79(3)
4.2 Canonical Transformation
82(6)
4.2.1 The Transformation Generating Function
84(2)
4.2.2 The Hamilton-Jacobi Equation (HJE)
86(1)
4.2.3 Time-Independent Hamilton-Jacobi Equation and Separation of Variables
87(1)
4.3 The Theory of Nonlinear Lattices
88(4)
4.3.1 The G2-Periodic Toda Lattice
91(1)
4.4 The Method of Characteristics for First-Order Partial-Differential Equations
92(5)
4.4.1 Characteristics for Quasi-Linear Equations
92(2)
4.4.2 Characteristics for the General First-Order Equation
94(2)
4.4.3 Characteristics for the Hamilton-Jacobi Equation
96(1)
4.5 Legendre Transform and Hopf-Lax Formula
97(4)
4.5.1 Viscosity Solutions of the HJE
99(2)
4.6 Notes and Bibliography
101(2)
5 State-Feedback Nonlinear H∞-Control for Continuous-Time Systems
103(34)
5.1 State-Feedback H∞-Control for Affine Nonlinear Systems
103(13)
5.1.1 Dissipative Analysis
111(4)
5.1.2 Controller Parametrization
115(1)
5.2 State-Feedback Nonlinear H∞ Tracking Control
116(3)
5.3 Robust Nonlinear H∞ State-Feedback Control
119(6)
5.4 State-Feedback H∞-Control for Time-Varying Affine Nonlinear Systems
125(2)
5.5 State-Feedback H∞-Control for State-Delayed Affine Nonlinear Systems
127(4)
5.6 State-Feedback H∞-Control for a General Class of Nonlinear Systems
131(1)
5.7 Nonlinear H∞ Almost-Disturbance-Decoupling
132(4)
5.8 Notes and Bibliography
136(1)
6 Output-Feedback Nonlinear H∞-Control for Continuous-Time Systems
137(38)
6.1 Output Measurement-Feedback H∞-Control for Affine Nonlinear Systems
137(14)
6.1.1 Controller Parameterization
147(4)
6.2 Output Measurement-Feedback Nonlinear H∞ Tracking Control
151(2)
6.3 Robust Output Measurement-Feedback Nonlinear H∞-Control
153(5)
6.3.1 Reliable Robust Output-Feedback Nonlinear H∞-Control
155(3)
6.4 Output Measurement-Feedback H∞-Control for a General Class of Nonlinear Systems
158(8)
6.4.1 Controller Parametrization
162(4)
6.5 Static Output-Feedback Control for Affine Nonlinear Systems
166(7)
6.5.1 Static Output-Feedback Control with Disturbance-Attenuation
169(4)
6.6 Notes and Bibliography
173(2)
7 Discrete-Time Nonlinear H∞-Control
175(30)
7.1 Full-Information H∞-Control for Affine Nonlinear Discrete-Time Systems
175(13)
7.1.1 State-Feedback H∞-Control for Affine Nonlinear Discrete-Time Systems
182(2)
7.1.2 Controller Parametrization
184(4)
7.2 Output Measurement-Feedback Nonlinear H∞-Control for Affine Discrete-Time Systems
188(6)
7.3 Extensions to a General Class of Discrete-Time Nonlinear Systems
194(3)
7.3.1 Full-Information H∞-Control for a General Class of Discrete-Time Nonlinear Systems
194(2)
7.3.2 Output Measurement-Feedback H∞-Control for a General Class of Discrete-Time Nonlinear Systems
196(1)
7.4 Approximate Approach to the Discrete-Time Nonlinear H∞-Control Problem
197(7)
7.4.1 An Approximate Approach to the Discrete-Time State-Feedback Problem
198(3)
7.4.2 An Approximate Approach to the Discrete-Time Output Measurement-Feedback Problem
201(3)
7.5 Notes and Bibliography
204(1)
8 Nonlinear H∞-Filtering
205(44)
8.1 Continuous-Time Nonlinear H∞-Filtering
205(9)
8.1.1 Infinite-Horizon Continuous-Time Nonlinear H∞-Filtering
210(3)
8.1.2 The Linearized Filter
213(1)
8.2 Continuous-Time Robust Nonlinear H∞-Filtering
214(3)
8.3 Certainty-Equivalent Filters (CEFs)
217(5)
8.3.1 2-DOF Certainty-Equivalent Filters
220(2)
8.4 Discrete-Time Nonlinear H∞-Filtering
222(10)
8.4.1 Infinite-Horizon Discrete-Time Nonlinear H∞-Filtering
227(1)
8.4.2 Approximate and Explicit Solution
228(4)
8.5 Discrete-Time Certainty-Equivalent Filters (CEFs)
232(9)
8.5.1 2-DOF Proportional-Derivative (PD) CEFs
235(2)
8.5.2 Approximate and Explicit Solution
237(4)
8.6 Robust Discrete-Time Nonlinear H∞-Filtering
241(7)
8.7 Notes and Bibliography
248(1)
9 Singular Nonlinear H∞-Control and H∞-Control for Singularly-Perturbed Nonlinear Systems
249(20)
9.1 Singular Nonlinear H∞-Control with State-Feedback
249(5)
9.1.1 State-Feedback Singular Nonlinear H∞-Control Using High-Gain Feedback
252(2)
9.2 Output Measurement-Feedback Singular Nonlinear H∞-Control
254(2)
9.3 Singular Nonlinear H∞-Control with Static Output-Feedback
256(2)
9.4 Singular Nonlinear H∞-Control for Cascaded Nonlinear Systems
258(5)
9.5 H∞-Control for Singularly-Perturbed Nonlinear Systems
263(5)
9.6 Notes and Bibliography
268(1)
10 H∞-Filtering for Singularly-Perturbed Nonlinear Systems
269(12)
10.1 Problem Definition and Preliminaries
269(1)
10.2 Decomposition Filters
270(8)
10.3 Aggregate Filters
278(1)
10.4 Examples
279(1)
10.5 Notes and Bibliography
280(1)
11 Mixed H2/H∞ Nonlinear Control
281(22)
11.1 Continuous-Time Mixed H2/H∞ Nonlinear Control
281(10)
11.1.1 The Infinite-Horizon Problem
287(2)
11.1.2 Extension to a General Class of Nonlinear Systems
289(2)
11.2 Discrete-Time Mixed H2/H∞ Nonlinear Control
291(8)
11.2.1 The Infinite-Horizon Problem
297(2)
11.3 Extension to a General Class of Discrete-Time Nonlinear Systems
299(2)
11.4 Notes and Bibliography
301(2)
12 Mixed H2/H∞ Nonlinear Filtering
303(30)
12.1 Continuous-Time Mixed H2/H∞ Nonlinear Filtering
303(12)
12.1.1 Solution to the Finite-Horizon Mixed H2/H∞ Nonlinear Filtering Problem
305(5)
12.1.2 Solution to the Finite-Horizon Mixed H2/H∞ Nonlinear Filtering
310(3)
12.1.3 Certainty-Equivalent Filters (CEFs)
313(2)
12.2 Discrete-Time Mixed H2/H∞ Nonlinear Filtering
315(14)
12.2.1 Solution to the Finite-Horizon Discrete-Time Mixed H2/H∞ Nonlinear Filtering Problem
317(4)
12.2.2 Solution to the Infinite-Horizon Discrete-Time Mixed H2/H∞ Nonlinear Filtering Problem
321(2)
12.2.3 Approximate and Explicit Solution to the Infinite-Horizon Discrete-Time Mixed H2/H∞ Nonlinear Filtering Problem
323(4)
12.2.4 Discrete-Time Certainty-Equivalent Filters (CEFs)
327(2)
12.3 Example
329(2)
12.4 Notes and Bibliography
331(2)
13 Solving the Hamilton-Jacobi Equation
333(34)
13.1 Review of Some Approaches for Solving the HJBE/HJIE
333(8)
13.1.1 Solving the HJIE/HJBE Using Polynomial Expansion and Basis Functions
336(5)
13.2 A Factorization Approach for Solving the HJIE
341(9)
13.2.1 Worked Examples
345(5)
13.3 Solving the Hamilton-Jacobi Equation for Mechanical Systems and Application to the Toda Lattice
350(6)
13.3.1 Solving the Hamilton-Jacobi Equation
350(4)
13.3.2 Solving the Hamilton-Jacobi Equation for the A2-Toda System
354(2)
13.4 Notes and Bibliography
356(11)
A Proof of Theorem 5.7.1
359(4)
B Proof of Theorem 8.2.2
363(4)
Bibliography 367(18)
Index 385
Ecole Polytechnique, Montreal, Canada
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